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Popular >

simplify 5ln(3)-2ln(3)+2ln(4)

Solution

simplify

5 ln (3) - 2 ln (3) + 2 ln (4)

Solution

ln (432)

+1

Decimal Notation

6.06842 \dots

Solution steps

5 ln (3) - 2 ln (3) + 2 ln (4)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (3) = ln (3^{2})

= 5 ln (3) - ln (3^{2}) + 2 ln (4)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (4) = ln (4^{2})

= 5 ln (3) - ln (3^{2}) + ln (4^{2})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (4^{2}) - ln (3^{2}) = ln (\frac{4 ^{2}}{3 ^{2}})

= 5 ln (3) + ln (\frac{4 ^{2}}{3 ^{2}})

\frac{4 ^{2}}{3 ^{2}} = \frac{16}{9}

= 5 ln (3) + ln (\frac{16}{9})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

5 ln (3) = ln (3^{5})

= ln (3^{5}) + ln (\frac{16}{9})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (3^{5}) + ln (\frac{16}{9}) = ln (3^{5} \cdot \frac{16}{9})

= ln (3^{5} \cdot \frac{16}{9})

3^{5} \cdot \frac{16}{9} = 432

= ln (432)

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Frequently Asked Questions (FAQ)

What is 5ln(3)-2ln(3)+2ln(4) ?
The solution to 5ln(3)-2ln(3)+2ln(4) is ln(432)